Publication list for Steve Butler

2022

1. Hadamard diagonalizable graphs of order at most 36 (with Jane Breen, Melissa Fuentes, Bernard Lidický, Michael Phillips, Alexander W. N. Riasanovksy, Sung-Yell Song, Ralihe R. Villagrán, Cedar Wiseman, and Xiaohong Zhang), Electronic Journal of Combinatorics 29 (2022) #P2.16, 22 pps.

2. A selected bibliography of Ron Graham, in Number Theory and Combinatorics. A Collection in Honor of the Mathematics of Ronald Graham, B. Landman, F. Luca, M. Nathanson, J. Nešetřil, and A. Robertson, eds., De Gruyter, 2022.

3. Working with Ron Graham, in Number Theory and Combinatorics. A Collection in Honor of the Mathematics of Ronald Graham, B. Landman, F. Luca, M. Nathanson, J. Nešetřil, and A. Robertson, eds., De Gruyter, 2022.

4. Spectral properties of the exponential distance matrix, (with Elizabeth Cooper, Aaron Li, Kate Lorenzen, Zoë Schopick), Involve 15 (2022), 739-762.

2020

1. The mathematical life of Fan Chung, AMS Notices 67 (2020), 327-335.

2. The inverse eigenvalue problem of a graph: Multiplicities and minors, (with Wayne Barrett, Shaun Fallat, Tracy Hall, Leslie Hogben, Jephian Lin, Bryan Shader, and Michael Young), JCTB 142 (2020), 276-306. [doi:10.1016/j.jctb.2019.10.005]

3. A jaunt in spectral graph theory, 50 Years of Combinatorics, Graph Theory, and Computing, F. Chung, R. Graham, F. Hoffman, L. Hogben, R. Mullin, D. West, eds. CRC Press, 2020, 213-238.

4. Counting tilings by taking walks in a graph, (with Jason Ekstrand and Stephen Osborne), A Project-Based Guide to Undergraduate Research in Mathematics, P. E. Harris, E. Insko, A. Wootton, eds. Springer, 2020, 153-176.

5. Enumerating parking completions using Join and Split, (with Ayomikun Adeniran, Galen Dorpalen-Barry, Pamela E. Harris, Cyrus Hettle, Qingzhong Liang, Jeremy L. Martin, Hayan Nam), Electronic Journal of Combinatorics 27 (2020), #P2.44, 19 pps. [doi:10.37236/9194]

6. Properties of a q-analogue of zero forcing, (with Craig Erickson, Shaun Fallat, H. Tracy Hall, Brenda Kroschel, Jephian C.-H. Lin, Bryan Shader, Nathan Warnberg, and Boting Yang), Graphs and Combinatorics 36 (2020), 1401-1419.

2018

1. A forest building process on simple graphs, (with Zhanar Berikkyzy, Jay Cummings, Kristin Heysse, Paul Horn, Ruth Luo, and Brent Moran), Discrete Mathematics 341 (2018), 497-507. [doi:10.1016/j.disc.2017.09.017]

2. Apollonian ring packings, (with Adrian Bolt, and Espen Hovland), in Connections in Discrete Mathematics, S. Butler, J. Cooper, G. Hurlbert, eds. Cambridge University Press, 283-296.

3. Permutations resilient to deletions, (with Noga Alon, Ron Graham, and Utkrisht Rajkumar), Annals of Combinatorics 22 (2018), 673-680. [doi:10.1007/s00026-018-0403-3]

2016

1. Symmetric 0-1 matrices with inverses having two distinct values and constant diagonal, (with Wayne Barrett and Tracy Hall), Linear Algebra and Its Applications 491 (2016), 41-55. [doi:10.1016/j.laa.2015.02.019]

2. The enhanced principal rank characteristic sequence, (with Minnie Catral, Shaun Fallat, Tracy Hall, Leslie Hogben, Pauline van den Driessche, and Michael Young), Linear Algebra and Its Applications 498 (2016), 181-200. [doi:10.1016/j.laa.2015.03.023]

3. Inserting plus signs and adding, (with Ron Graham and Richard Stong), American Mathematical Monthly 123 (2016), 274-279.[doi:10.4169/amer.math.monthly.123.3.274]

4. Algebraic aspects of the normalized Laplacian, in Recent Trends in Combinatorics, Andrew Beveridge, Jerrold Griggs, Leslie Hogben, Gregg Musiker, and Prasad Tetali, eds., Springer, 2016, 295-315.

5. The mathematics of the flip and horseshoe shuffles, (with Persi Diaconis and Ron Graham), American Mathematical Monthly 123 (2016), 542-556. [doi:10.4169/amer.math.monthly.123.6.542]

6. A cospectral family of graphs for the normalized Laplacian found by toggling, (with Kristin Heysse), Linear Algebra and its Applications 507 (2016), 499-512. [doi:10.1016/j.laa.2016.06.033]

7. Rainbow arithmetic progressions, (with Craig Erickson, Leslie Hogben, Kirsten Hogenson, Lucas Kramer, Richard L. Kramer, Jephian Chin-Hung Lin, Ryan R. Martin, Derrick Stolee, Nathan Warnberg, and Michael Young), Journal of Combinatorics 7 (2016), 595-626. [doi:10.4310/JOC.2016.v7.n4.a3]

8. Counting prime juggling patterns, (with Esther Banaian, Christopher Cox, Jeffrey Davis, Jacob Landgraf, and Scarlitte Ponce), Graphs and Combinatorics 32 (2016), 1675-1688. [doi:10.1007/s00373-016-1711-1].

2014

1. Tiling a strip with triangles, (with John Bodeen, Taekyoung Kim, Xiyuan Sun, and Shenzhi Wang), Electronic Journal of Combinatorics 21 (2014), P1.7, 15pp.

2. Counting tilings by taking walks, (with Steven Osborne), The Journal of Combinatorial Mathematics and Combinatorial Computing 88 (2014), 83-94.

3. The maximum nullity of a complete subdivision graph is equal to its zero forcing number, (with Wayne Barrett, Minnie Catral, Shaun Fallat, Tracy Hall, Leslie Hogben, and Michael Young), The Electronic Journal of Linear Algebra 27 (2014), 444-457. [doi:10.13001/1081-3810.1629]

4. The principal rank characteristic sequence over various fields, (with Wayne Barrett, Minnie Catral, Shaun Fallat, Tracy Hall, Leslie Hogben, Pauline van den Driessche, and Michael Young), Linear Algebra and Its Applications 459 (2014), 222-236. [doi:10.1016/j.laa.2014.06.045]

5. de Bruijn sequences with varying combs, (with Abbas Alhakim and Ron Graham), INTEGERS: The Electronic Journal of Combinatorial Number Theory 14A (2014) A1, 23 pp.

6. Unrolling residues to avoid progressions, (with Ron Graham and Linyuan Lu), Mathematics Magazine 87 (2014), 83-94. [doi:10.4169/math.mag.87.2.83]

7. Numerical tic-tac-toe on the 4x4 board, (with Bryce Sandlund, Kerrick Staley, and Michael Dixon), COCOON 2014, LNCS 8591, Springer-Verlag, 537-546. [doi:10.1007/978-3-319-08783-2_46]

8. Spectral graph theory, (with Fan Chung), in Handbook of Linear Algebra, second edition, Leslie Hogben ed., 14pp.

9. A gentle introduction to the normalized Laplacian, IMAGE 53 (Fall 2014), 19-27.

2012

1. Origami rings, (with Joe Buhler, Warwick de Launey, and Ron Graham), Journal of the Australian Mathematical Society 92 (2012), 299-311. [doi:10.1017/S1446788711001741]

2. A note on marking lines in [k]^n, (with Ron Graham), Designs, Codes and Cryptography 65 (2012), 165-175. [doi:10.1007/s10623-011-9507-z]

3. Computing inertia sets using atoms, (with Wayne Barrett, Tracy Hall, John Sinkovic, Wasin So, Colin Starr, and Amy Yielding), Linear Algebra and its Applications 436 (2012), 4489-4502. [doi:10.1016/j.laa.2011.08.026]

2010

1. Finding patterns avoiding many monochromatic constellations, (with Kevin Costello and Ron Graham), Experimental Mathematics 19 (2010), number 4, 399-411. [doi:10.1080/10586458.2010.10390631]

2. Iterated triangle partitions, (with Ron Graham), Fete of Combinatorics and Computer Science, G. Katona, A. Schrijver, T. Szonyi, eds., Bolyai Society Mathematical Studies 29, Springer-Verlag, Heidelberg (2010), 23-42. [doi:10.1007/978-3-642-13580-4_2]

3. Tiling polygons with lattice triangles, (with Fan Chung, Ron Graham, and Miklos Laczkovich), Discrete & Computational Geometry 44 (2010), 896-903. [doi:10.1007/s00454-010-9249-0]

4. Irreducible Apollonian configurations and packings, (with Ron Graham, Gerhard Guettler, and Colin Mallows), Discrete & Computational Geometry 44 (2010), 487-506. [doi:10.1007/s00454-009-9216-9]

5. Eigenvalues of 2-edge-coverings, Linear and Multilinear Algebra 58 (2010), 413-423.[doi:10.1080/03081080802622694]

6. Shuffling with ordered cards, (with Ron Graham), Journal of Combinatorics 1 (2010), 121-139. [doi:10.4310/JOC.2010.v1.n2.a3]

7. Enumerating (multiplex) juggling sequences, (with Ron Graham), Annals of Combinatorics 13 (2010), 413-424. [doi:10.1007/s00026-009-0040-y]

8. Small spectral gap in the combinatorial Laplacian implies Hamiltonian, (with Fan Chung), Annals of Combinatorics 13 (2010), 403-412. [doi:10.1007/s00026-009-0039-4]

9. Intersecting domino tilings, (with Paul Horn and Eric Tressler), The Fibonacci Quarterly 48 (2010), 114-120.

10. How to play the majority game with a liar, (with Ron Graham and Jia Mao), Discrete Mathematics 310 (6 February 2010), 622-629. [doi:10.1016/j.disc.2009.05.011]

11. A note on nested sums, (with Pavel Karasik), Journal of Integer Sequences 13 (2010), article 10.4.4, 8 pp.

12. A note about cospectral graphs for the adjacency and normalized Laplacian matrices, Linear and Multilinear Algebra 58 (2010), 387-390. [doi:10.1080/03081080902722741]

2008

1. Hat guessing games, (with Mohammad Hajiaghayi, Robert Kleinberg, and Tom Leighton), SIAM Journal on Discrete Mathematics 22 (2008), 592-605. [doi:10.1137/060652774]; Republished in SIAM Review 51 (2009), 399-413. [doi:10.1137/080743470]

2. Jumping sequences, (with Ron Graham and Nan Zang), Journal of Integer Sequences 11 (2008), 13 pp.

3. Estimating the number of graphs containing very long induced paths, Ars Combinatoria 88 (2008), 321-332.

4. Zero forcing sets and the minimum rank of graphs, (with AIM minimum rank-special graphs work group), Linear Algebra and its Applications 428 (2008), 1628-1648. [doi:10.1016/j.laa.2007.10.009]

2006

1. Relating singular values and discrepancy of weighted directed graphs, Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm (Miami, FL, 2006), 1112-1116. [doi:10.1145/1109557.1109680]

2. Using discrepancy to control singular values for nonnegative matrices, Linear Algebra and its Applications 419 (2006), 486-493. [doi:10.1016/j.laa.2006.05.015]

Books

1. Rudiments of Ramsey Theory, second edition, (with Ron Graham), CBMS 123, AMS press, 2015.

Miscellaneous writings and musings

• Eigenvalues and structures of graphs, Ph.D dissertation, written under the direction of Fan Chung.

• Bounding the number of graphs containing very long induced paths, MS Thesis, written under the direction of Wayne Barrett

• Determining the underlying functions for Cauchy power and exponential forms, research done as an undergraduate student

• Tangent line transformations, research done as an undergraduate student

• Posed problems (Monthly #11030, #11265; Math Magazine #1668, #1730, #1761, #Q1008)

• Mathematical card tricks based on determining a deck knowing only two cards, summary of work done for freshman honors project in 2022

Memories about Ron Graham

• The Mathematical Showman - Ron Graham (1935-2020) - Numberphile Podcast

• Getting to work with Ron Graham (a blog post)

• Ron Graham has left (as Tom Odda, Jr), MAA FOCUS, Aug/Sep 2020, 8-9

• The passing of Ron Graham, Annals of Combinatorics 24 (2020), 619-621

In September 2006 I visited the Center for Combinatorics at Nankai University and gave a series of three lectures.  The notes for these lectures are given here.

• Three common spectra

• Applications of Courant-Fischer

• Cheeger constants and discrepancy

In April 2011 I gave a guest lecture about cospectral graphs at UCSD.  The notes for this lecture is given here.

• Cospectral graphs

Some proofs without words (or not very many).

• Property of the GCD;  Moebius transform of the triangular numbers;  Tiling Aztec diamonds with skinny strips

Various bits and pieces.

• Method for doing the (approximate) Markov chains for bisection of angles

• A property of positive semidefinite matrices

Contributions to the Gathering for Gardner over the years.

• Backwards addition

• Collapsing numbers in base 2, 3, and beyond

• Tiling Tetris boards

• A card trick inspired by perfect shuffling

Letter to the editor of school newspaper written as an undergraduate.